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प्रश्न
State Kepler's laws of planetary motion.
उत्तर
Kepler’s first law (Law of orbit):
Every planet revolves around the sun in an elliptical orbit with the sun situated at one of the focii of the ellipse
Kepler’s second law (Law of equal areas):
The radius vector drawn from the sun to any planet sweeps out equal areas in equal intervals of time, i.e., areal velocity of the radius vector is constant.
Kepler’s third law (Law of periods):
The square of the period of revolution of the planet round the sun is directly proportional to the cube of the semi-major axis of the elliptical orbit
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संबंधित प्रश्न
State Kepler's law of orbit and law of equal areas.
Let the period of revolution of a planet at a distance R from a star be T. Prove that if it was at a distance of 2R from the star, its period of revolution will be \[\sqrt{8}\] T.
Identify the law shown in the figure and state three respective laws.
In the Following figure shows the elliptical path of a planet about the sun. The two shaded parts have equal area. If t1 and t2 be the time taken by the planet to go from a to b and from c to d respectively,
Answer the following question.
State Kepler’s law of equal areas.
Answer the following question.
State Kepler’s law of the period.
The square of its period of revolution around the sun is directly proportional to the _______ of the mean distance of a planet from the sun.
The third law of Kepler is also known as the Law of ______.
State Kepler’s laws.
If the distance between the sun and the earth is made three times, then attraction between the two will ______
The mass and radius of earth is 'Me' and 'Re' respectively and that of moon is 'Mm' and 'Rm' respectively. The distance between the centre of the earth and that of moon is 'D'. The minimum speed required for a body (mass 'm') to project from a point midway between their centres to escape to infinity is ______.
The earth moves around the sun in an elliptical orbit as shown in the figure. The ratio, `"OA"/"OB"` = x. The ratio of the speed of the earth at Band at A is ______.
If the sun and the planets carried huge amounts of opposite charges ______.
- all three of Kepler’s laws would still be valid.
- only the third law will be valid.
- the second law will not change.
- the first law will still be valid.
The centre of mass of an extended body on the surface of the earth and its centre of gravity ______.
- are always at the same point for any size of the body.
- are always at the same point only for spherical bodies.
- can never be at the same point.
- is close to each other for objects, say of sizes less than 100 m.
- both can change if the object is taken deep inside the earth.
Draw areal velocity versus time graph for mars.
What is the direction of areal velocity of the earth around the sun?
A star like the sun has several bodies moving around it at different distances. Consider that all of them are moving in circular orbits. Let r be the distance of the body from the centre of the star and let its linear velocity be v, angular velocity ω, kinetic energy K, gravitational potential energy U, total energy E and angular momentum l. As the radius r of the orbit increases, determine which of the above quantities increase and which ones decrease.
A satellite is in an elliptic orbit around the earth with aphelion of 6R and perihelion of 2 R where R= 6400 km is the radius of the earth. Find eccentricity of the orbit. Find the velocity of the satellite at apogee and perigee. What should be done if this satellite has to be transferred to a circular orbit of radius 6R ?
[G = 6.67 × 10–11 SI units and M = 6 × 1024 kg]
The maximum and minimum distances of a comet from the Sun are 1.6 × 1012 m and 8.0 × 1010 m respectively. If the speed of the comet at the nearest point is 6 × 104 ms-1, the speed at the farthest point is ______.
lf the angular momentum of a planet of mass m, moving around the Sun in a circular orbit is L, about the center of the Sun, and its areal velocity is ______.
Two planets A and B of equal mass are having their period of revolutions TA and TB such that TA = 2TB. These planets are revolving in the circular orbits of radii rA and rB respectively. Which out of the following would be the correct relationship of their orbits?
